To get the Teslagun you need to turn the power on, right outside of the power room, in the courtyard, interact with the Teslagun that's sitting on the Workbench. This will enable the 3 generators around the map. Do these specific steps until the lights are green.

GENERATORS:

1. Location Courtyard: Kill zombies near the generator using a Pack-a-Punch'd weapon with Dead Wire.
2. Location Field (shortcut leading up to Tractor Shed, spawn): Kill dogs near the generator.
3. Location Prison Exterior (near the Sledgehammer): Kill enemies with Thundergun.

After all 3 Generators have been filled with enough zombies, the lights will turn green and you'll be able to claim the Teslagun from the workbench.

Video of my playthrough: https://www.youtube.com/watch?v=iSVaIoXGzFE

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